A model of the self-organization of synapses in the visual cortex is presented.
Subject to Hebbian learning with decay, evolution of synaptic strengths
proceeds to a stable state in which all synapses have either maximum, or minimum,
pre/post-synaptic coincidence. The most stable configuration gives rise to
anatomically realistic "local maps", each of macro-columnar size, and each organized
as Möbius projections of retinotopic space. A tiling of V1, constructed
of approximately mirror-image reﬂections of each local map by its neighbours is
formed, accounting for orientation-preference singularities, linear zones, and saddle
points - with each map linked by connections between sites of common orientation
preference. Ocular dominance columns, the occurrence of direction preference fractures
always in odd numbers around singularities, and effects of stimulus orientation
relative to velocity of motion, are accounted for. Convergence to this configuration
is facilitated by the spatio-temporal learning rule.